You seem to have a good understanding of some key concepts here. You know the term "reserve." A person's pitch will rise as they approach reserve (aka run out of breath). If counting without stuttering, most people can count out loud to 20 before *needing* a breath. We can also use up all of our air on one stuttered word. ​ It helps also that you have it isolated to /h/ and /i/. Have you ever done voluntary stuttering? In your case you would do pseudo prolongations to learn how to terminate your elongation quickly and well before reserve and vocal pitch rise. You can use a stretch band if it helps. Take the word "hello." You would start the "he" > stop your voice > then say "hello". A mirror may help a lot. good luck